On Representation Spaces

Jose G. Anaya; Felix Capulin; Enrique Castaneda-Alvarado; W. J. Charatonik; Fernando Orozco-Zitli

doi:10.1016/j.topol.2013.08.012

On Representation Spaces

Jose G. Anaya
, Felix Capulin
, Enrique Castaneda-Alvarado
, W. J. Charatonik
, Fernando Orozco-Zitli

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Let C be a class of topological spaces, let P be a subset of C , and let α be a class of mappings having the composition property. Given X ∈ C , we write X ∈ C l α ( P ) if for every open cover U of X there is a space Y ∈ P and a U -mapping &fnof;: X → Y that belongs to α . The closure operator Cl α defines a topology τ α in C. After proving general properties of the operator Cl α , we investigate some properties of the topological space (&naturals;, τ α ), where &naturals; is the space of all nondegenerate metric continua and α is one of the following classes: all mappings, confluent mappings, or monotone mappings.

Original language	American English
Journal	Topology and its Applications
Volume	164
DOIs	https://doi.org/10.1016/j.topol.2013.08.012
State	Published - Mar 1 2014

Keywords

Arcwise connected
Chainability
Confluent mapping
Inverse limit
Local connected
ε-Map

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1016/j.topol.2013.08.012

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title = "On Representation Spaces",

abstract = " Let C be a class of topological spaces, let P be a subset of C , and let \α be a class of mappings having the composition property. Given X \∈ C , we write X \∈ C l \α ( P ) if for every open cover U of X there is a space Y \∈ P and a U -mapping \&fnof;: X \→ Y that belongs to \α . The closure operator Cl \α defines a topology \τ \α in C. After proving general properties of the operator Cl \α , we investigate some properties of the topological space (\&naturals;, \τ \α ), where \&naturals; is the space of all nondegenerate metric continua and \α is one of the following classes: all mappings, confluent mappings, or monotone mappings.",

keywords = "Arcwise connected, Chainability, Confluent mapping, Inverse limit, Local connected, ε-Map",

author = "Anaya, \{Jose G.\} and Felix Capulin and Enrique Castaneda-Alvarado and Charatonik, \{W. J.\} and Fernando Orozco-Zitli",

year = "2014",

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doi = "10.1016/j.topol.2013.08.012",

language = "American English",

volume = "164",

journal = "Topology and its Applications",

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TY - JOUR

T1 - On Representation Spaces

AU - Anaya, Jose G.

AU - Capulin, Felix

AU - Castaneda-Alvarado, Enrique

AU - Charatonik, W. J.

AU - Orozco-Zitli, Fernando

PY - 2014/3/1

Y1 - 2014/3/1

N2 - Let C be a class of topological spaces, let P be a subset of C , and let α be a class of mappings having the composition property. Given X ∈ C , we write X ∈ C l α ( P ) if for every open cover U of X there is a space Y ∈ P and a U -mapping &fnof;: X → Y that belongs to α . The closure operator Cl α defines a topology τ α in C. After proving general properties of the operator Cl α , we investigate some properties of the topological space (&naturals;, τ α ), where &naturals; is the space of all nondegenerate metric continua and α is one of the following classes: all mappings, confluent mappings, or monotone mappings.

AB - Let C be a class of topological spaces, let P be a subset of C , and let α be a class of mappings having the composition property. Given X ∈ C , we write X ∈ C l α ( P ) if for every open cover U of X there is a space Y ∈ P and a U -mapping &fnof;: X → Y that belongs to α . The closure operator Cl α defines a topology τ α in C. After proving general properties of the operator Cl α , we investigate some properties of the topological space (&naturals;, τ α ), where &naturals; is the space of all nondegenerate metric continua and α is one of the following classes: all mappings, confluent mappings, or monotone mappings.

KW - Arcwise connected

KW - Chainability

KW - Confluent mapping

KW - Inverse limit

KW - Local connected

KW - ε-Map

UR - https://scholarsmine.mst.edu/math_stat_facwork/885

UR - https://doi.org/10.1016/j.topol.2013.08.012

U2 - 10.1016/j.topol.2013.08.012

DO - 10.1016/j.topol.2013.08.012

M3 - Article

VL - 164

JO - Topology and its Applications

JF - Topology and its Applications

ER -

On Representation Spaces

Abstract

Keywords

Disciplines

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